This Article 
 Bibliographic References 
 Add to: 
A Markov Pixon Information Approach for Low-Level Image Description
June 1999 (vol. 21 no. 6)
pp. 482-494

Abstract—The problem of extracting information from an image which corresponds to early stage processing in vision is addressed. We propose a new approach (the MPI approach) which simultaneously provides a restored image, a segmented image and a map which reflects the local scale for representing the information. Embedded in a Bayesian framework, this approach is based on an information prior, a pixon model and two Markovian priors. This model based approach is oriented to detect and analyze small parabolic patches in a noisy environment. The number of clusters and their parameters are not required for the segmentation process. The MPI approach is applied to the analysis of Statistical Parametric Maps obtained from fMRI experiments.

[1] R.K. Pina and R.C. Puetter, "Bayesian Image Reconstruction: The Pixon and Optimal Image Modeling," P.A.S.P., vol. 105, pp. 630-637, 1993.
[2] R.C. Puetter and R.K. Pina, "The Pixon and Bayesian Reconstruction," SPIE, vol. 1,946, pp. 405-416, 1993.
[3] T.R. Metcalf, H.S. Hudson, T. Kosugi, R.C. Puetter, and R.K. Pina, "Fractal Pixon Image Reconstruction for Yohkoh's Hard X-Ray Telescope," Ap. J., vol. 466, pp. 585-594, 1996.
[4] C.E. Shannon, "A Mathematical Theory of Communication," Bell Systems Technical J., vol. 27, p. 379, 1948.
[5] S.F. Gull and J. Skilling, "Maximum Entropy Method in Image Processing," Proc. Inst. Elec. Eng. F, vol. 131, pp. 646-659, 1984.
[6] B.R. Frieden, "Restoring With Maximum Likelihood and Maximum Entropy," J. Optical Soc. Amer., vol. 62, pp. 511-518, 1972.
[7] A.K.C. Wong and P.K. Sahoo, "A Gray-Level Thresholding Selection Method Based on Maximum Entropy Principle," IEEE Trans. Systems Man and Cybernetics, vol. 19, pp. 866-871, 1989.
[8] J. Besag, "Spatial Interaction and Statistical Analysis of Lattice Systems," Acad. Royal Statistical Soc., Series B, vol. 36, pp. 721-741, 1974.
[9] S. Geman and D. Geman, "Stochastic Relaxation, Gibbs Distribution, and the Bayesian Restoration of Images," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721-741, 1984.
[10] H. Derin and H. Elliott, "Modelling and Segmentation of Noisy and Textured Images Using Gibbs Random Fields," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 9, no. 1, pp. 39-55, Jan. 1987.
[11] D. Geman and G. Reynolds, "Constrained Restoration and the Recovery of Discontinuities," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 14, pp. 367-383, 1992.
[12] S. Lakshmanan and H. Derin, “Simultaneous Parameter Estimation and Segmentation of Gibbs Random Fields Using Simulated Annealing,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 11, pp. 799-813, 1989.
[13] C.S. Won and H. Derin, "Unsupervised Segmentation of Noisy and Textured Images Using Markov Random Fields," Computer Vision Graphics and Image Processing, vol. 4, pp. 308-328, 1992.
[14] Z. Liang, J.R. MacFall, and D.P. Harrington, "Parameter Estimation and Tissue Segmentation From Multispectral MR Images," IEEE Trans. Medical Imaging, vol. 13, no. 3, pp. 441-449, 1994.
[15] X. Descombes, J.F. Mangin, E. Pechersky, and M. Sigelle, "Fine Structures Preserving Model for Image Processing," Proc. Ninth SCIA 95, pp. 349-356,Uppsala, Sweden, 1995.
[16] X. Descombes, R. Morris, J. Zerubia, and M. Berthod, "Estimation of Markov Random Field Prior Parameters Using Markov Chain Monte Carlo Maximum Likelihood," IEEE Trans. Image Processing, in press.
[17] A.I. Khinchin, Mathematical Foundations of Information Theory.Dover, 1957.
[18] R.C. Puetter, "Pixon-Based Multiresolution Image Reconstruction and the Quantification of Picture Information Content," Int'l J. Image Systems and Technologies, vol. 6, pp. 314-331, 1995.
[19] B.S. Manjunath and R. Chellappa, “Unsupervised Texture Segmentation Using Markov Random Field Models,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 13, pp. 478-482, 1991.
[20] X. Descombes, R. Morris, and J. Zerubia, "Quelques améliorations la segmentation d'images bayesienne. Première partie: Modélisation," Traitement du Signal, vol. 14, no. 4, pp. 373-382, 1997.
[21] K.J. Worsley, A.C. Evans, S. Marret, and P. Neelin, "A Three-Dimensional Statistical Analysis for CBF Activation Studies in Human Brain," J. Cerebral Blood Flow and Metabolism, vol. 12, pp. 900-918, 1992.
[22] K.J. Friston, K.J. Worsley, R.S.J. Frackowiak, J.C. Mazziotta, and A.C. Evans, "Assessing the Significance of Focal Activations Using Their Spatial Extent," Human Brain Mapping, vol. 1, pp. 210-220, 1994.
[23] K.J. Friston, A.P. Holmes, J.B. Poline, P.J. Grasby, S.C.R. Williams, R.S.J. Frackowiak, and R. Turner, "Analysis of fMRI Time-Series Revisited," NeuroImage, vol. 2, pp. 45-53, 1995.
[24] K.J. Worsley and K.J. Friston, "Analysis of fMRI Time-Series Revisited Again," NeuroImage, vol. 2, pp. 173-181, 1995.
[25] N. Lange, "Tutorial in Biostatistics: Statistical Approaches to Human Brain Mapping by fMRI," Statistics in Medicine, vol. 15, pp. 389-428, 1996.
[26] S. Rabe-Hesketh, E.T. Bullmore, and M.J. Brammer, "The Analysis of Functional Magnetic Resonance Images," Statistical Methods in Medical Research, vol. 6, pp. 215-237, 1997.
[27] E.T. Bullmore, M.J. Brammer, S.C.R. Williams, S. Rabe-Hesketh, N. Janot, A.S. David, J.D.C. Mellers, R. Howard, and P. Sham, "Statistical Methods of Estimation and Inference for Functional MR Image Analysis," Magnetic Resonance in Medicine, vol. 35, pp. 261-277, 1996.
[28] X. Descombes, F. Kruggel, and D.Y. von Cramon, "Spatio-Temporal fMRI Analysis Using Markov Random Fields," IEEE Trans. Medical Imagery, vol. 17, no. 6, pp. 1,028-1,039, Dec. 1998.
[29] F. Kruggel, X. Descombes, and Y.D. Von Cramon, "Preprocessing of fMR Datasets," IEEE Workshop on Biomedical Image Analysis, Santa Barbara, Calif., 1998. Los Alamitos, Calif.: IEEE CS Press, 1998.
[30] A.M. Thompson, J.C. Brown, J.W. Kay, and D.M. Titterington, "A study of methods of choosing the smoothing parameter in image restoration by regularization," IEEE Trans. Pattern Anal. Machine Intell., vol. 13, no. 4, pp. 326-339, Apr. 1991.

Index Terms:
Information, Pixon, Markov Random Fields, image restoration, fMRI analysis.
Xavier Descombes, Frithjof Kruggel, "A Markov Pixon Information Approach for Low-Level Image Description," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 21, no. 6, pp. 482-494, June 1999, doi:10.1109/34.771311
Usage of this product signifies your acceptance of the Terms of Use.